Question

The surface area of a solid metallic sphere is $616c{m}^2$. It is melted and recast into a smaller sphere of diameter 3.5 cm. How many can such spheres be obtained? [4 MARKS]

Answer 1

Formula: 1 Mark
Application: 1 Mark
Solution: 2 Marks

Let R be the radius of the solid metallic sphere.
Then, its surface area is given by,
$4\pi R^2=616$ [Given]
$\Rightarrow 4\times \frac{22}{7}\times R^2=616$
$\Rightarrow R^2=\frac{616\times 7}{4\times 22}=49\Rightarrow R=\sqrt{49}$
= 7 cm.
$\therefore$ Number of small spheres formed
$=\frac{Totalvolumeofsolidmetallicsphere}{Volumeofasmallmetallicsphere}$
$=\frac{\frac{4}{3}\pi (7{)}^3}{\frac{4}{3}\pi {\left(\frac{7}{4}\right)}^3}=64$
Hence, 64 small spheres can be obtained.